Wigan host the Hammers this weekend and Martinez feels his counterpart has all the attributes to test himself away from the English game.
"People have a certain perception of Sam," the Wigan boss told The Daily Mail.
"There is a forward-thinking side to him that would make him well-suited to managing on the continent.
"That approach was very evident when he was in charge at Bolton, where he introduced sports science and other methods for bringing the best out of players.
"Maybe people don't always expect that from him, but when you dig a little deeper, you see he has that side to him.
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"He has incredible experience in the game, and he is very curious about all those different percentages that can help players perform at the very peak of their powers. That is a very continental approach."
Allardyce utilised that experience when rejuvenating the careers of seasoned professionals while he was in charge at Bolton, and Martinez is full of praise for that Trotters team.
The former Swansea manager said: "Just look at that team he put together at Bolton, with the likes of Djorkaeff, Campo, Okocha and Hierro.
"You have to be something special as a manager to understand all those different cultures and mould them into a successful unit, but Sam did that by leading them into the Europa League."
That progressive approach convinces Spaniard Martinez that the ex-Bolton boss could go anywhere and be successful.
He said: "If he can do that, he can go anywhere in the world and manage even the most multi-cultural dressing room without any problem.
"I don't know how Sam would cope with the language in Spain, but if he really does fancy giving it a go in La Liga one day, he has all the attributes to do it."